A wider view

Paul Dirac developed a beautiful mathematical representation of quantum mechanics based on the principle of superposition of states of a physical system. The principle is a statement of the central feature of quantum mechanics, that an unobserved physical system can be considered as existing in a number of possible states all at once. When a measurement is made the system 'jumps' into a new state in which it has the measured value of the relevant physical quantity.

Dirac's idea was to represent the state of a physical system by a vector in a space of many dimensions. The components of the vector along the many directions would then represent the various possible results of physical measurement.

Just as an 'ordinary' vector has three independent components, along the x, y, and z axes, Dirac's 'state vector' has many,

Paul Dirac (1902-1984)

possibly even an infinite number of, components in the many directions of Dirac's mathematical space. This representation of quantum mechanics is now generally known as Dirac's generalised transformation theory, because it involves transforming the coordinate axes to look at the state vector from different frames of reference.

The representations of Heisenberg and Schrodinger fell in neatly, as special cases within Dirac's scheme, which then became, and still remains, the most complete and the most general theory of quantum mechanics.